Metro will consider offering New York City-style unlimited monthly passes in concert with fare increases after its board of directors expressed concern Thursday that riders are too dissatisfied with the rail system’s performance to pay more without new incentives.

A proposal submitted by agency management last week called for attempting to balance the system’s budget for the next fiscal year largely by raising fares during off-peak times, when trains run infrequently. It will do away with the “peak of the peak” surcharge at the height of rush hour instituted in 2010.

“The off-peak experience is getting excruciating, and it seems like putting them through the ringer to make them pay more for single-tracking and episodic service,” said Tom Downs, a board member representing the District.

Several board members said monthly passes would keep riders from fleeing the system for the roads because they would find value in taking Metro for more of their trips.

“I think our customers are not too happy with the system, and so this monthly fare may be a good idea,” D.C. board member Tom Bulger said.

Metro’s chief executive officer also intends to make hefty new fees on riders using paper farecards a key component of the agency’s revenue — even as the system aggressively works to eliminate the use of those cards. All paper-based rush-hour trips would be $6; non-rush hour trips would be $4.

“I think we need to make sure we don’t create a monster that we can’t afford when people stop using paper,” said Mortimer Downey, a federal government representative on the board.

As Metro moves away from demand-based pricing for rail, officials are exploring ways to confront parking imbalances, with Metro staff proposing more, and cheaper, reserved spaces that are held each morning for their owner at a monthly rate. As many as 30 percent of a station’s parking spaces could be reserved until 10 a.m. — a cutoff that some board members said should be made earlier if prices are to be lowered.

Daily parking rates would rise by 25 cents, while monthly reservations could fall from $65 to $45.

Alvin J. Nichols, a Maryland board member, said end-of-the-line riders are “hostage” to parking garages and not necessarily able to pay more despite intense demand.

“My understanding of economics is, if all the spots are gone by 7 a.m., you could probably charge more,” D.C. Council member Muriel Bowser said.